Neutral (on average) Fitness

 Stochasticity is paramount in the neutral case with  μ = a = 0

 For   D = 0   demographic and seascape noise lead to very different outcomes:

Demographic stochasticity draws in the distribution to (a delta-function at) the absorbing state y=0

Seascape fluctuations leads to a log-normal distribution with variance of  log(y) growing or decaying (linearly) in time.

 For   D ≠ 0   (first taking   N →∞)  migration from the mean of population acts as a source that counteracts absorption to y=0

      remains fixed to initial value.

For demographic noise, this leads to a steady state

While for seascape fluctuations, the steady state is

 The power-law tail of the distribution for seascape fluctuations can lead to broad distributions:

 Steady-state is somewhat of a misnomer as the power-law tail forms and extends over time, such that

Next (Extinction on seascape) Outline Introduction Mean field approach Neutral landscape Extinction on a seascape Growth on seascape Summary